By Bernard Etkin
Aimed toward upper-level undergraduates, graduate scholars, and execs, this article matters the dynamics of atmospheric flight, with specialise in aircraft balance and regulate. an intensive set of numerical examples covers STOL airplanes, subsonic jet transports, hypersonic flight, balance augmentation, and wind and density gradients. The ebook includes 260 illustrations.
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Extra info for Dynamics of Atmospheric Flight
Equilibrium is a special case of such a solution. In this special case the Lyapunov definition is as follows. Let 6 and E be the radii of two hyperspheres in state space with centers at the equilibrium point, symbolically represented in two dimensions in Fig. 3d. These surfaces are such that for all initial states lying inside S, the subsequent solution lies for all time inside S,. Then the origin is a stable point if there exists a 6 > 0 for all E > 0, no matter how small E becomes. That is, the solution can be made arbitrarily small by choosing the initial conditions small enough.
N+(V) which is plotted in Pig. 11. DISTRIBUTION OF PEAKS It is observed that for the larger values of v most, but not all, local maxima are immediately preceded by a positive event as defined above. This is illustrated in Fig. 4 where the events are defined by the line I . 6,43) can also be interpreted as a good approximation to the number of peaks per unit time that are greater than v . It follows that the distribution of peaks per unit time is given approximately by and has the form shown on Fig.
6,51a) is a particular case of the Poisson distribution, for zero events in a time t,. A more rigorous treatment of survival probability covering nonstationary and non-Gaussian processes is given by Rice and Beer (ref. 8) and is applied to launch vehicles by Beer and Lennox (ref. 9). 13 Failure probability. DISCUSSION OF CONDITION (ii) We return now to the condition of statistical independence of adjacent intervals. This implies that the joint probability f (v,, v,) = f (v,)f (v,) where v, and v, are values of the variable during two adjacent intervals A,t and A,t, as illustrated in Pig.